Nonlinear Engineering 2021; 10: 395–403
Weihua Yin* and Li Lin
Study on vibration monitoring and anti-vibration
of overhead transmission line
https://doi.org/10.1515/nleng-2021-0031
Received Jun 9, 2021; accepted Jul 30, 2021.
Abstract: Numerous forms of dampers are used to eliminate the vibrations in transmission lines. In the contemporaneous editorial, a survey has been done on vibrations monitoring and anti-vibration of overhead transmission line of transmission lines having multiple dampers
for dissimilar cable sizes. To investigate the outcome of
the position of dampers on extreme strains created in the
line. A comprehensive survey of the extreme strains created is also made for several wind power input conventions. A finite element technique is used to measure the frequency and manner figures of the cable with and without
a damper. The response of the bare conductor, loaded conductor, the conductor for various dampers’ location is also
studied. Spoilers and torsional dampers are maximum actual in diminishing electrode galloping, while dampers are
quite the utmost effectual plans for aeolian shakings and
spiral dampers are admirable for identical lesser width of
electrodes.
Keywords: transmission line, anti-vibration, vibration,
spiral vibration, dampers, aeolian
1 Introduction
The enticement of wind is caused for wind vibration of
overhead transmission lines. It indemnities conductors,
equipment, and towers, which may be the reason fire
and protection of public’s life and goods [1]. Dampers are
extensively used in transmission lines to diminish wind
shaking levels to the safe level. The quantity and loca-
*Corresponding Author: Weihua Yin, Hunan Provincial Key Laboratory of Grids Operation and Control on Multi-Power Sources Area,
Shaoyang 422000, China
Shaoyang University, Shaoyang 422000, China,
E-mail: weihuaweihuayin@gmail.com
Li Lin, Hunan Provincial Key Laboratory of Grids Operation and Control on Multi-Power Sources Area, Shaoyang 422000, China
Shaoyang University, Shaoyang 422000, China, E-mail:
li5865819@gmail.com
Open Access. © 2021 Weihua Yin et al., published by De Gruyter.
alone 4.0 License.
tion of dampers on transmission lines are mostly resolute by investigated on the foundation of the energy balance principle [2]. The run-through particularly cannot
precisely deliberate the end product of fixing the position
of dampers and their active features. A proportion of hypothetical investigation about dampers. Nevertheless, it immobile seems broken stocks, the defeat of damper hammers, stern bending of steel strand produced by the wind
shaking in genuine engineering. The inland investigation
on joined shaking of transmission line and damper system is not sufficient [3]. The outcomes are not beneficial
to industrial applications and absence active computeraided design series around wind shaking. To eliminate
vacillations in overhead transmission lines dampers are
used transmission lines. Because of laminar wind, overhead transmission lines will be agitated [4]. Oscillations
can lead to harm to the conductor. To diminish these vibrations and oscillations to an indiscriminating dimension,
curbing systems will have to be connected in the overhead transmission lines. A Stockbridge damper is a modified mass damper used to eliminate wind-induced shakings on trim constructions for example above power lines
and extended cantilevered signs. The dumbbell-shaped
convenient contains dual masses at the culmination of a
small dimension of cable or elastic pole, which is compressed at its internal to the foremost cable. The damper
is designed to dispel the vitality of oscillations in the key
cable to a satisfactory level. Its idiosyncratic figure provides it the name “dog-bone damper” [5]. To neutralize
vibrations animated by the wind, supposed Karman vibrations. Contingent on the form of the rod, numerous
damper kinds with numerous dissimilar simulations are
obtainable. The term of the damper is because of the researcher H. Stockbridge [6], who progressive the extension of the damper in the 1920s. Spacers assist to create
expanse among the limited conductors of a bundle line
to avert the conductors from bumping together. Therefore
evade damage done to conductors. Spacer dampers will
be used if vibrations animated by wind need to be predictable. Damping [7] essentials amid the frame and the
conductor clamps, the vibration generosities of the conductor can be abridged to a credulous facet. Numerous dissimilar prototypes of the inserts are obtainable for dissimilar bundle preparations. Wind-induced quivering [8] of
This work is licensed under the Creative Commons Attribution
396 | Weihua Yin and Li Lin, Study on vibration monitoring and anti-vibration of overhead transmission line
the above conductors is conjoint worldwide and can reason conductor exhaustion nearby a hardware supplement.
The essential for the transmission of message signals rise,
several Optical Ground Wires (OPWG) are changing outdated ground wires. All Aluminum Alloy Conductors [9]
(AAAC) have been a current optimal for the above conductors because of the compensations in both electrical and
motorized features. Inappropriately AAAC is recognized to
be disposed to Aeolian vibration. Shaking dampers are extensively used to mechanism aeolian shaking of the conductors and earth wires containing OPGW [10? –13]. Figure 1 shows the Spiral vibration damper. The high tension to mass ratio allows AAAC conductors to be pass
through at advanced tension and extended spans than outdated ACSR (Aluminum Conductor Steel Reinforced) conductors. Inopportunely the self-damping of the conductor
declines as tension rises. The wind control into the conductor rises with span dimension. Hereafter AAAC conductors are probable to involve more unembellished shaking
than ACSR.
Figure 1: Spiral vibration damper
The essential for the transmission of message signals
rise, several Optical Ground Wires (OPWG) are changing
outdated ground wires. All Aluminum Alloy Conductors
(AAAC) have been a current optimal for the above conductors because of the compensations in both electrical
and motorized features [12]. A comprehensive survey of
the extreme strains created is also made for several wind
power input conventions. A finite element technique is
used to measure the frequency and manner figures. This
study aims to investigate the suppression schemes for a
large crossing span of UHV eight-bundle conductor aeolian vibration.
1. First, the general conception of aeolian and the analytical models for the conductor, vibration-dampers,
and damping wire is demonstrated.
2. Second, the equation of the energy balance method is
introduced and terms in the equation are determined.
The article is thus organized in the following order.
Literature reviews of various techniques and precession
farming are detailed in Section 2. Section 3 discusses the
vibration equation and model analysis. Methods of vibration control are discussed in section 4. The use of a damper
is discussed in section 5. Finally, the manuscript is concluded in Section 6.
2 Literature review
The aeolian vibration of ground wires proceeds abode
in a broad frequency varies of 6.3 to 111 Hz, contingent
on the geometric airstream speed and ground wire constraints. Besides, a slightly stable airstream can reason
aeolian shaking at a consistent frequency. Aeolian shaking is categorized by extended period. Understanding land
and meteorological conditions demonstration that there
can be extreme shaking at any instant in lines placed in
level and blustery areas. Dampers were extensively used
to overwhelm the aeolian shaking on above-ground wires
meanwhile in the 1950s, which rough copy map. It is consists of three portions as presented [13]. The dampers show
significant consequences to destroy the aeolian shaking,
though approximately restrictions are accessible communication system. Anti-vibration influence is not perfect.
The superior frequency of the ground wires on transmission lines with a size below 100 mm2 is normally above
100 Hz that needs the damper’s extra broad resonance
frequency range. While the FG-type damper has individual dual significance frequencies for its regular loads [14].
When the shaking frequency of the ground wires surpasses the frequency in smooth and blustery areas. The
crushed wires at the clamp happen bulge and exhaustion
breaking may happen [15]. The compress effortlessly slipups the grasp consequence on ground wires is not real
since its iron-plate kind clamp holds the ground wires by
revenue of the line interaction nearly. The clamp moveable owing to material move stealthily, which may reason
ground wires smashing if not attached suitably [17]. Messenger cables are effortlessly stained. The tack hammer
dampers are empty-cylinder type, its envoy cords are in
biochemical and manual incorporation erosion in wide period because air pollution and another force act. The erosion will lead to the forte and inflexibility abridged and the
resistance reduced. So the mallets are informal to sag afterward durable process and the anti-shaking consequence
Weihua Yin and Li Lin, Study on vibration monitoring and anti-vibration of overhead transmission line | 397
decay extremely [18]. To attain the finest anti-shaking result of the damper, it should be the code that the dispatch
rider cables can crop extreme ricochet to ingest extra vitality in the assortment and fixing of the damper. Consequently, the ordinary frequency of the inhibition must be
well-suited with the probable shaking frequency varies of
the above lines to drive when shaking happens [19]. Typically impediments on EHV lines cannot destroy aeolian
shaking well, so inhibitions with improved intended construction and a better frequency vary essential to be advanced as a spare for dampers. The damper, with adjustment fork-molded mallet and indiscretion abidance, was
recognized [20]. The bulk of mallet and measurement of
the envoy wires on the dual margins of fastening are unequal. An extra consequence can be attained by mixture
inhibition.
To come across the greater necessities of shaking conquest in the Hexi lines, two types of FR-type inhibition
with a mound hold were recognized. Figure 2 shows the
general flow chart for the optimization of a Stockbridge
damper. Initially, the frequency was intended rendering to
the line factors and climate. Then, the impediments were
envisioned creating on practices and philosophy [21].
Thirdly, type trials were done and improvement was
comprehended. A photo of the novel damper is obtainable in Figure 3. The mound clamp clenches the ground
wire. During galloping, conductors at the suspension insulators can move along the line with amplitudes of up
to 1 m, depending on insulator length. Thus, if not long
enough to accommodate such motion, the ground lead
will be stressed by these repeated movements. Stressrelieving clamp designs such as over armor rods reduce local stresses in-ground leads while some utilities even use a
polymeric insulator in parallel with the slack ground lead
to relieve strain associated with conductor and ground
lead motions due to wind. That type of configuration has
offered reliable long-term performance at the cost of only
an additional 230 kV polymeric insulator, energized only
if the arrester fails. This is the same configuration as the
insulated hanger for distribution arrester designs
Figure 2: General flow chart for the optimization of a Stockbridge
damper
to a few meters [23]. Figure 4 shows the Stress investigation of the vibration conductor. The transmission line is
abridged as an extended solid cylinder, whose symmetrical and substantial goods unaffected end-to-end extent of
the transmission line and twisting inflexibility unnoticed.
Therefore, the transmission line’s vibration equation underneath the accomplishment of straight wind is engraved
as Eq. (2).
3 Vibration equation and model
analysis
The transmission line can be elementary as tensioning
beam with minor difficulty, and shaking. The equation can
be inscribed as Eq. (1) [22]. The cord shaking model is secondhand to feign transmission line disregarding cable rigorousness as the extent of a transmission line is equal
Figure 3: The novel Stockbridge damper ing (a) and (b).
398 | Weihua Yin and Li Lin, Study on vibration monitoring and anti-vibration of overhead transmission line
∂2 y
∂4 y
∂2 y c∂y
−T 2 =
+m 2 +
4
∂t
∂x
∂t
∂t
X
∂2 y
∂2 y c∂y
−T 2 =
p(t) +
δ(x − x i )f i (t)m 2 +
∂t
∂t
∂t
4 Result and discussion
EI
p(t) +
i=1
n
X
δ(x − x n )f n (t)
(1)
i=1
The component rigorousness matrix and
matrix are articulated.

C1 0 0 C1 0 0
 0 0 0 0 0 0


AE  0 0 0 0 0 0
Ke =

L  C1 0 0 C1 0 0

 0 0 0 0 0 0
0 0 0 0 0 0

0
0
0
0
0
 0 C2
0
0 −C2


0
C2 0
0
F 0
Se = 
L 0
0
0
0
0

 0 −C2
0
0
0
0
0
−C2 0
0
strain stiffness





,



0
0
−C2
0
0
C2









(2)
Them is excellence of constituent length of line, Y is the
movement of wind shaking, c is checking constant, T is
normal stiffness, p(t) is excitation force, x is longitudinal organizes lengthways, n(x) is the position of the Nth
damper, N f (t)is the consequence of dampers, Q is trim
force, M is winding instant, A is the area, F is the amount
of component early pretentiousness and additional axial
force, L is the measurement of the unit, 1 C is ductile and
condensation stiffness number, 2 C is stress arduousness
constant. Once the unit draws, both 1 C and 2 C value1.0,
when the unit is pushed, together 1 C and 2 C value 0.0
Figure 4: Stress investigation of vibration conductor
Prevalent approaches of plummeting vibrations of power
line performers can be alienated as follows: sleek structural approaches and mechanical approaches. Normally
used apparatus for damping in the airpower line conductor vibrations comprises dampers of type Stockbridge, spiral dampers, torsional dampers, and spacers with damping possessions. Designated, actual mechanical dampers
are labeled underneath. Stockbridge dampers are the utmost regularly used inhibitions on above your head power
lines [24]. A typical Stockbridge damper contains dual ‘inertial masses’ fastened at the split ends of a mainly proposed small steel cord strand involved with a fasten to
the checked conductor [25]. The dynamism of ambiances
is degenerate over resistance caused by slippage among
the messenger wires. When the damper is located on a vibrating conductor, the erect motion of the heaviness forces
the steel conductor to bend, producing friction among the
wires which dissolves the energy. The weights and damper
geometrics affect the measure of energy degenerate for exact vibration occurrences [26]. A better form of the definitive damper topographies two dissimilar masses in the
form of a bell, situated unevenly at the finishes of a steel
galvanized messenger of perchance the best energy debauchery possessions [27]. Such a design of the damper
doubles the number of character peaks from two obtained
with the classic version of the Stockbridge damper to four
in the improved version [28]. Modern Stockbridge dampers
are envisioned for real energy assignment and debauchery
for the entire spectrum of frequencies inside aeolian vibrations. To confirm actual damping, the first damper should
be situated next to the supplement inside the shortest loop
which is shaped at the maximum speed of wind (7 m/s).
The Spiral Damper has been practical on minor diameter
conductors (≤ 19 mm) for over 30 years. It is complete of
uneven non-metal substantial in the technique of spiral of
length 1.2 – 1.5 m, with an interior diameter beyond the
conductor diameter. A spiral at the one end observes strappingly to the conductor [29–32]. Throughout aeolian vibrations, the restraining part of this spiral influences the conductor and reasons creation of impulses that upset conductor vibrations. An additional type of spiral hindrance
is the Air Flow Spoiler. The Detuning Pendulum is used for
single cables and cables in a bundle. A typical design of the
damper is a weight attached to a cable or cable bundle. The
length of the arm and weight depends mainly on the cable
diameter and span length. Arm length and mass mandatory to the overwhelmed instant of ice and wind load, thus
diminishing galloping. This damper separates frequencies
Weihua Yin and Li Lin, Study on vibration monitoring and anti-vibration of overhead transmission line |
of vertical vibrations from frequencies of torsional vibrations. Three-four dampers are connected along the span,
using braids to decrease local cable tensions. It syndicates
belongings of a torsional damper and detunes [33]. This
damper uses a torsional motion of a conductor during galloping to damper vibrations and improves its effectiveness
by separating frequencies of vertical vibrations from frequencies of torsional vibrations, as in pendulum dampers.
This damper upsurges the worth of hustle of wind, overhead which galloping happens, and decreases its amplitudes.
For controlling galloping for single conductors and
for controlling aeolian vibrations (in conductors of small
diameters and spans) can be used AR Twister dampers.
Three types of AR Twisters are manufactured: Piston,
Kanister, and Slider Twisting is the main technique for
galloping control in all these dampers. All AR Twister
dampers reduce or eliminate galloping of a conductor by
making the conductor rotate and – as a consequence –
decrease the aerodynamic lift. The AR Twister is an inertial device made of [33]. Damping required to control aeolian vibrations is achieved by rubbing metal with metal,
as a result of slight motions between the device body and
its clamp. These devices are rigidly fixed to the conductor
with standard vertical clamps or clamps which are angled
at 45 ◦ to 60 ◦ . Such an arrangement of dampers causes an
initial torsion of the conductor under gravity forces. In the
event of galloping, inertial forces affect the device making
the conductor twist again, in the opposite direction to its
initial position.
399
Figure 6: Shuddering retort of a archetypal extent length of transmission line
Figure 7: Corroboration for the full conductor (Ld = ¼ Lc)
Figure 8: Meandering strain of a characteristic extent length of
transmission line
Figure 5: Corroboration for the undecorated electrode
Table 1 and 2 show the: high-performance conductors and their specifications. When galloping, torsional
oscillations increase, ice sediment is distributed over the
greater surface of the conductor and the profile becomes
smooth and less eccentric. At the same time, the aerodynamic lift force is reduced and the level of vibrations decreases. It is perceived from Figure 5 that the vigor balance
scheme overvalues the retort of the unembellished electrode, through Figure 6 specifies that it underrates the re-
400 | Weihua Yin and Li Lin, Study on vibration monitoring and anti-vibration of overhead transmission line
Table 1: High performance conductors and its specifications
Conductor cross
section & type
Standard
ACSR
20/35
EN 50182
ACSR
300/50
EN 50182
ACSR
680/85
EN 50182
AAAC
120
EN 50182
AAAC
185
EN 50182
Construction
(n×mm)
Diameter (mm)
Weight (kg/km)
Breaking
load
(min)
Max. ratio (tension
to weight)
26×3.2al
7×2.49 St
20.3
844.1
73.36
26×3.86 Al
7×3.0 St
24.4
1227.3
105.09
54×4.0 Al
19×2.4 St
36
2549.7
206.25
19×2.8
37×2.5
AAAAC
241
SS 4240811
&
SS 4240812
19×4.02
14
321.2
34.51
17.5
500.3
53.58
20.1
663
61.6
Before creep:
2100
After creep
1670
Before creep:
2100
After creep
1670
Before
creep:
2100
After creep
1670
Before
creep:
2100
After creep
1780
Before creep:
2100
After creep
1780
Regular Suspension clamps will
include rods
Suspension
clamps shall be
AGS type
Length of the armor rod
Wedge
tension
clamp
Post
insulators
distribution ties
+
-
-
Before
creep:
1230
After
creep
1100
-
-
-
-
+
+
-
-
+
1930
1700
2235
-
-
1524
+
+
+
+
+
+
-
-
-
Length is
600mm
Length
900mm
tort of the encumbered conductor. The conspiracies in Figures 5 and 6 also demonstrate that the proportion of the
trembling amplitude to the excitation force knowingly reductions with cumulative frequency. Though, the shuddering response of the electrode with the involved Stockbridge
damper is much inferior to that of the naked conductor.
For an excitation frequency of f ¼26.5 Hz, Figure 7 demonstrates the period retort turn of the electrode for numerous dampers’ locations. The vibration amplitude is suggestively concentrated by attaching a Stockbridge damper at
mid-span. A span length of Lc¼ 366m is designated for
the subsequent mathematical instance. This miscellany
confirms that the relation of the electrode slump to span
length is characteristic of the prevailing transmission line.
The equivalent wind force F0¼ 370.9 N. Figure 8 largess
the no dimensional retort of the conductor. It is perceived
that the electrode retort reduces when the Stockbridge inhibition is attached except for f ¼12.19 Hz which demonstrations a minor surge in the anode retort. The cause for
this upsurge is as the position of the impediment for this
exact frequency resembles a knob.
is
-
5 Applications of dampers
Permitting to the concert features of the ground wire
damper and mound damper, shared with involvement in
the joining of ground wire dampers, the novel inhibitions
were fit in agreement with the next values [33].
1. Ground wires in individual circuit lines, one FR-2
damper was predisposed on apiece cross of the extents
below 300 m;
2. One FR-2 and one FR-3 damper
3. One FR-3 damper and two FR-2 dampers
The detachment among together dampers was 0.75 m,
with an equivalent detachment among fitted dampers.
1. For ground wires in dual circuit lines, one FR-2 and FR3 damper were close-fitting on spans below 300 m, and
expedients that joint damper and damping cable were
equestrian on spans above 300 m.
In total, above 12 000 sets of mound inhibitions were
used from the foot by mound armor stick, it suitable, se-
Weihua Yin and Li Lin, Study on vibration monitoring and anti-vibration of overhead transmission line | 401
Table 2: Specification NCS 163 for Stockbridge type vibration dampers for distribution and transmission overhead lines
Conductor cross
& type
Standard
Construction
Diameter
Cross
section
of
conductor
(mm2 )
Breaking load
(kN)
Max. ratio (tension to weight)
Suspension
clamps shall be
AGS type
Suspension
clamps shall be
AGS type
Length of the armor rod
Wedge tension
clamp
Tension shall be
with helical end
type
AAAC AL59
593
SS 4240813
&
SS 4240813
61×3.52mm
31.7
593.6
AAAC AL59
774
SS 4240813
&
SS 4240814
61×4.02mm
36.2
774.2
AAAC AL59
362
EN50182
AAAC AL59
118
Specification
NCS-8
OPGW
245
Specification
NCS-8
37×3.52mm
24.71
362.1
14.84±0.26
118
20.58±0.36
245
143
178
86.91
40
70
Before creep:
2100
After creep
1670
Before creep:
2100
After creep
1670
Before creep:
1230
After creep
1100
Before creep:
2100
After creep
1780
-
-
-
+
Before
creep:
2100
After creep
1780
-+
+
+
-
-
+
2235
2235
1140
1550
+
+
1700
+
+
+
-
-
-
-
-
cure, and slip-resistant. Since the novel clamp averts stress
absorption by armor rod in its place of a screw, it can
diminution subtleties bendy straining at the clamp.
6 Conclusions
Shakings of above power line conductors produced by
airstream may cause their obliteration. Consequently,
decreasing the near of such feelings is significant owing
to care of the whole edifice. Communal approaches of
deprecation of conductor sensations are unreceptive:
good decisive of the exterior shallow of an electrode, a
good proposal of the self-damping and use of unusual
hindering devices, contingent on the kind of excitations.
Now, there is no one way to entirely diminish shakings
through galloping, for which amplitudes may spread
high standards. Permitting to the investigation works.
Spoilers and torsional dampers are maximum actual
in diminishing electrode galloping, while dampers are
quite the utmost effectual plans for aeolian shakings and
spiral dampers are admirable for identical lesser width of
electrodes. It is also perceived that the supplement of the
Stockbridge damper significantly decreases the trembling
retort of the electrode. The grade of decrease needs on the
position and the figure of the Stockbridge damper. Now,
there is invincible to entirely decrease ambiances through
galloping, for which amplitudes may spread high morals.
Airflow spoilers and torsional curbs are of utmost actual
in diminishing electrode galloping, while Stockbridge
inhibitions are immobile the supreme effectual plans for
aeolian ambiances and spiral hindrances are brilliant for
actual minor width of electrodes. A new area of research
that can be analyzed with the better control algorithm
with the suitable dampers and actuators for the outrigger structural control. The adaptive control, stochastic
optimal control, and robust control techniques can be
incorporated for the control of the damped outrigger
structure and other structural forms with the big data
techniques involved in the performance improvement of
the tall building vibration control techniques.
402 | Weihua Yin and Li Lin, Study on vibration monitoring and anti-vibration of overhead transmission line
Acknowledgements: Key R&D Project of Hunan Provincial Department of Science and Technology (2018GK2033).
Funding information: The authors state no funding
involved.
Author contributions: All authors have accepted responsibility for the entire content of this manuscript and
approved its submission.
Conflict of interest: The authors state no conflict of interest.
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